A sign at the base of the tree revealed its identity and also made mention of the great "Arbol del Tule" in Santa Maria de Tule (Oaxaca, Mexico) which is both the worldwide champion of this species and the tree with the largest girth in the world (as claimed by some).
The leaves of this tree are similar to those of the Yew tree and thus the similarity in the scientific names between Taxodium and Taxus. These same leaves also help distinguish this tree from true cypress trees that have a similar "cone" but a very different leaf.
The image below does not really do justice to this tree as it is quite a bit bigger than it looks in this picture. I´m not really sure why the metallic fence but I suppose that it is there to keep people from climbing up onto the large lower branches.
The bark of the Montezuma Cypress reminds me a bit of what I imagine what dragon scales would look like.
Here is a rough translation of the sign by this tree...
"This specimen in the Retiro park is possibly the oldest tree in the park or even in all of Madrid. It was planted around the year 1633. It is said that during the War of Independence the French troops installed an artillery piece in its trunk, which may be the reason this tree was spared when almost all of the trees of the Retiro were cut down to make room for the French military headquarters. In 1991 the metallic fence was installed to protect this fine specimen. The "Ahuehuete del Parterre", as this tree is called, is the only representative of this species in the Retiro park and has been included in the registry of singular trees of Madrid."